On solvability of a nonlinear problem in theory of income distribution. (English) Zbl 1258.45004

This paper considers a nonlinear integro-differential equation with a Hammerstein type noncompact operator, arising in the theory of income distribution. It proves the existence of a positive solution of the nonlinear problem in Sobolev space \(W_1^1(\mathbb R^+)\). Some examples arising in applications are shown. For one modeling problem a uniqueness theorem is proved. At the end of the paper the results of numerical calculations are given.
Reviewer: Li Xing (Yinchuan)


45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
45M20 Positive solutions of integral equations
65R20 Numerical methods for integral equations